1. Field of the Invention
The present invention relates generally to a space-time-frequency block coding apparatus in a transmitter with three transmit (Tx) antennas, and in particular, to an apparatus for transmitting an input symbol sequence through three Tx antennas using a selected transmission matrix in order to improve the performance of a space-time-frequency block code (STFBC).
2. Description of the Related Art
The fundamental issue in communications is how efficiently and reliably data is transmitted on the channels. As future-generation multimedia mobile communications require high-speed communication systems capable of transmitting a variety of information including video and wireless data beyond the voice-focused service, it is important to increase system efficiency through the use of a channel coding method suitable for the system.
In the wireless channel environment of a mobile communication system, as opposed to a wired channel environment, a transmission signal inevitably experiences loss due to several factors such as multipath interference, shadowing, wave attenuation, time-variant noise, and fading. The information loss causes a severe distortion to the transmission signal, degrading the entire system performance. In order to reduce the information loss, many error control techniques are usually adopted to increase system reliability. One of these techniques is to use an error correction code.
Multipath fading is reduced through the use of diversity techniques in the wireless communication system. The diversity techniques are, for example, time diversity, frequency diversity, and antenna diversity.
Antenna diversity uses multiple antennas. This diversity scheme is further divided into receive (Rx) antenna diversity using a plurality of Rx antennas, Tx antenna diversity using a plurality of Tx antennas, and multiple-input multiple-output (MIMO) using a plurality of Tx antennas and a plurality of Rx antennas.
The MIMO is a special case of space-time coding (STC) that extends the coding of the time domain to the space domain by the transmission through a plurality of Tx antennas of a signal encoded according to a set coding method, with the aim to achieve a lower error rate.
V. Tarokh, et al. proposed space-time block coding (STBC) as one of the methods to efficiently applying antenna diversity (see “Space-Time Block Coding from Orthogonal Designs”, IEEE Trans. On Info., Theory, Vol. 45, pp. 1456-1467, July 1999). The Tarokh STBC scheme is an extension of the transmit antenna diversity scheme of S. M. Alamouti (see, “A Simple Transmit Diversity Technique for Wireless Communications”, IEEE Journal on Selected Area in Communications, Vol. 16, pp. 1451-1458, October 1988), for two or more Tx antennas.
FIG. 1 is a block diagram of a transmitter in a mobile communication system using the conventional Tarokh's STBC scheme. The transmitter is comprised of a modulator 100, a serial-to-parallel (S/P) converter 102, an STBC coder 104, and four Tx antennas 106, 108, 110 and 112.
Referring to FIG. 1, the modulator 100 modulates input information data (or coded data) according to a modulation scheme. The modulation scheme can be one of binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), quadrature amplitude modulation (QAM), pulse amplitude modulation (PAM), and phase shift keying (PSK).
The S/P converter 102 parallelizes serial modulation symbols received from the modulator 100, s1, s2, S3, s4. The STBC coder 104 creates eight symbol combinations by STBC-encoding the four modulation symbols, s1, s2, s3, s4 and sequentially transmits them through the four Tx antennas 106 to 112. A coding matrix used to generate the eight symbol combinations is expressed as
                              G          4                =                  [                                                                      s                  1                                                                              s                  2                                                                              s                  3                                                                              s                  4                                                                                                      -                                      s                    2                                                                                                s                  1                                                                              -                                      s                    4                                                                                                s                  3                                                                                                      -                                      s                    3                                                                                                s                  4                                                                              s                  1                                                                              -                                      s                    2                                                                                                                        -                                      s                    4                                                                                                -                                      s                    3                                                                                                s                  2                                                                              s                  1                                                                                                      s                  1                  *                                                                              s                  2                  *                                                                              s                  3                  *                                                                              s                  4                  *                                                                                                      -                                      s                    2                    *                                                                                                s                  1                  *                                                                              -                                      s                    4                    *                                                                                                s                  3                  *                                                                                                      -                                      s                    3                    *                                                                                                s                  4                  *                                                                              s                  1                  *                                                                              -                                      s                    2                    *                                                                                                                        -                                      s                    4                    *                                                                                                -                                      s                    3                    *                                                                                                s                  2                  *                                                                              s                  1                  *                                                              ]                                    (        1        )            where G4 denotes the coding matrix for symbols transmitted through the four Tx antennas 106 to 112 and s1, s2, s3, s4 denote the input four symbols to be transmitted. The number of columns of the coding matrix is equal to the number of Tx antennas, and the number of rows corresponds to the time required to transmit the four symbols. Thus, the four symbols are transmitted through the four Tx antennas over eight time intervals.
Specifically, for a first time interval, s1 is transmitted through the first Tx antenna 106, s2 through the second Tx antenna 108, s3 through the third Tx antenna 110, and s4 through the fourth Tx antenna 112. In this manner, −s*4, −s*3, s*2, −s*1 are transmitted through the first to fourth Tx antennas 106 to 112, respectively, during an eighth time interval. That is, the STBC coder 104 sequentially provides the symbols of an ith column in the coding matrix to an ith Tx antenna.
As described above, the STBC coder 104 generates the eight symbol sequences using the four input symbols and their conjugates and negatives, and transmits them through the four Tx antennas 106 to 112 over eight time intervals. Since the symbol sequences for the respective Tx antennas, that is the columns of the coding matrix, are mutually orthogonal, a diversity gain equal to the diversity order can be achieved.
FIG. 2 is a block diagram of a receiver in the mobile communication system using the conventional STBC scheme. The receiver is the counterpart of the transmitter illustrated in FIG. 1.
The receiver is comprised of a plurality of Rx antennas 200 to 202, a channel estimator 204, a signal combiner 206, a detector 208, a parallel-to-serial (P/S) converter 210, and a demodulator 212.
Referring to FIG. 2, the first to Pth Rx antennas 200 to 202 provide signals received from the four Tx antennas of the transmitter illustrated in FIG. 1 to the channel estimator 204 and the signal combiner 206. The channel estimator 204 estimates channel coefficients representing channel gains from the Tx antennas 106 to 112 to the Rx antennas 200 to 202 using the signals received from the first to Pth Rx antennas 200 to 202. The signal combiner 206 combines the signals received from the first to pth Rx antennas 200 to 202 with the channel coefficients in a predetermined method. The detector 208 generates hypothesis symbols by multiplying the combined symbols by the channel coefficients, calculates decision statistics for all possible symbols transmitted from the transmitter using the hypothesis symbols, and detects the actual transmitted symbols through threshold detection. The P/S converter 210 serializes the parallel symbols received from the detector 208. The demodulator 212 demodulates the serial symbol sequence in a according to a demodulation method, thereby recovering the original information bits.
As stated earlier, the Alamouti STBC technique offers the benefit of achieving a diversity order equal to the number of Tx antennas, namely a full diversity order, without sacrificing the data rate by transmitting complex symbols through two Tx antennas only.
The Tarokh STBC scheme extended from the Alamouti STBC scheme achieves a full diversity order using an STBC in the form of a matrix with orthogonal columns, as described with reference to FIGS. 1 and 2. However, because four complex symbols are transmitted over eight time intervals, the Tarokh STBC scheme causes a half decrease in the data rate. In addition, since it takes eight time intervals to completely transmit one block with four complex symbols, reception performance is degraded due to channel changes within the block over a fast fading channel. In other words, the transmission of complex symbols through four or more Tx antennas requires 2N time intervals for N symbols, causing a longer latency and a decrease in the data rate.
To achieve a full rate in a MIMO system that transmits a complex signal through three or more Tx antennas, the Giannakis group presented a full-diversity, full-rate (FDFR) STBC for four Tx antennas using constellation rotation over a complex field.
FIG. 3 is a block diagram of a transmitter in a mobile communication system using the conventional Giannakis STBC scheme. As illustrated in FIG. 3, the transmitter includes a modulator 300, a pre-coder 302, a space-time mapper 304, and a plurality of Tx antennas 306, 308, 310 and 312.
Referring to FIG. 3, the modulator 300 modulates input information data (or coded data) according to a modulation scheme such as BPSK, QPSK, QAM, PAM or PSK. The pre-coder 302 pre-encodes Nt modulation symbols received from the modulator 300, d1, d2, d3, d4, such that signal rotation occurs in a signal space, and outputs the resulting Nt symbols. For notational simplicity, four Tx antennas are assumed. Let a sequence of four modulation symbols from the modulator 300 be denoted by d. The pre-coder 302 generates a complex vector r by computing the modulation symbol sequence, d using Equation (2).
                    r        =                              Θ            ⁢                                                  ⁢            d                    =                                                    [                                                                            1                                                                                      α                        0                        1                                                                                                            α                        0                        2                                                                                                            α                        0                        3                                                                                                                        1                                                                                      α                        1                        1                                                                                                            α                        1                        2                                                                                                            α                        1                        3                                                                                                                        1                                                                                      α                        2                        1                                                                                                            α                        2                        2                                                                                                            α                        2                        3                                                                                                                        1                                                                                      α                        3                        1                                                                                                            α                        3                        2                                                                                                            α                        3                        3                                                                                            ]                            ⁡                              [                                                                                                    d                        1                                                                                                                                                d                        2                                                                                                                                                d                        3                                                                                                                                                d                        4                                                                                            ]                                      =                          [                                                                                          r                      1                                                                                                                                  r                      2                                                                                                                                  r                      3                                                                                                                                  r                      4                                                                                  ]                                                          (        2        )            where Θ denotes a pre-coding matrix. The Giannakis group uses a unitary Vandermonde matrix as the pre-coding matrix. In the pre-coding matrix, αi is given asαi=exp(j2π(i+1/4)/4), i=0,1,2,3  (3)
The Giannakis STBC scheme uses four Tx antennas and is easily extended to more than four Tx antennas. The space-time mapper 304 STBC-encodes the pre-coded symbols according to the following method.
                    S        =                  [                                                                      r                  1                                                            0                                            0                                            0                                                                    0                                                              r                  2                                                            0                                            0                                                                    0                                            0                                                              r                  3                                                            0                                                                    0                                            0                                            0                                                              r                  4                                                              ]                                    (        4        )            where S is a coding matrix for symbols transmitted through the four Tx antennas 306 to 312. The number of columns of the coding matrix is equal to the number of Tx antennas, and the number of the rows corresponds to the time required to transmit the four symbols. That is, the four symbols are transmitted through the four Tx antennas over the four time intervals.
Specifically, for a first time interval, r1 is transmitted through the first Tx antenna 306, with no signals through the other Tx antennas 308, 310 and 312. For a second time interval, r2 is transmitted through the second Tx antenna 308, with no signals through the other Tx antennas 306, 310 and 312. For a third time interval, r3 is transmitted through the third Tx antenna 310, with no signals through the other Tx antennas 306, 308, and 312. For a fourth time interval, r4 is transmitted through the fourth Tx antenna 310, with no signals through the other Tx antennas 306, 308 and 310.
Upon receipt of the four symbols on a radio channel for the four time intervals, a receiver (not shown) recovers the modulation symbol sequence, d, by using maximum likelihood (ML) decoding.
Tae-Jin Jung and Kyung-Whoon Cheun proposed a pre-coder and a concatenated code with an excellent coding gain in 2003, compared to the Giannakis STBC. They enhance the coding gain by concatenating Alamouti STBCs instead of using a diagonal matrix proposed by the Giannakis group. For the sake of convenience, this STBC will be referred to as the “Alamouti FDFR STBC”.
FIG. 4 is a block diagram of a transmitter in a mobile communication system using the conventional Alamouti FDFR STBC and four Tx antennas. As illustrated in FIG. 4, the transmitter includes a pre-coder 400, a mapper 402, a delay 404, two Alamouti coders 406 and 408, and four Tx antennas 410, 412, 414 and 416.
Referring to FIG. 4, the pre-coder 400 pre-encodes four input modulation symbols, d1, d2, d3, d4, such that signal rotation occurs in a signal space. For the input of a sequence of the four modulation symbols, d, the pre-coder 400 generates a complex vector, r, by computing
                    r        =                              Θ            ⁢                                                  ⁢            d                    =                                                    [                                                                            1                                                                                      α                        0                        1                                                                                                            α                        0                        2                                                                                                            α                        0                        3                                                                                                                        1                                                                                      α                        1                        1                                                                                                            α                        1                        2                                                                                                            α                        1                        3                                                                                                                        1                                                                                      α                        2                        1                                                                                                            α                        2                        2                                                                                                            α                        2                        3                                                                                                                        1                                                                                      α                        3                        1                                                                                                            α                        3                        2                                                                                                            α                        3                        3                                                                                            ]                            ⁡                              [                                                                                                    d                        1                                                                                                                                                d                        2                                                                                                                                                d                        3                                                                                                                                                d                        4                                                                                            ]                                      =                          [                                                                                          r                      1                                                                                                                                  r                      2                                                                                                                                  r                      3                                                                                                                                  r                      4                                                                                  ]                                                          (        5        )            where αi=exp(j2π(i+1/4)/4), i=0,1,2,3.
The mapper 402 groups the four pre-coded symbols by twos and outputs two vectors each including two elements, [r1, r2]T and [r3, r4]T to the Alamouti coder 406 and the delay 404, respectively. The delay 404 delays the second vector [r3, r4]T for one time interval. Thus, the first vector [r1, r2]T is provided to the Alamouti coder 406 in a first time interval and the second vector [r3, r4]T is provided to the Alamouti coder 408 in a second time interval. The Alamouti coder refers to a coder that operates in the Alamouti STBC scheme. The Alamouti coder 406 encodes [r1, r2]T so that it is transmitted through the first and second Tx antennas 410 and 412 during the first and second time intervals. The Alamouti coder 408 encodes [r3, r4]T so that it is transmitted through the third and fourth Tx antennas 414 and 416 during the third and fourth time intervals. A coding matrix used to transmit the four symbols from the mapper 402 through the multiple antennas is
                    S        =                  [                                                                      r                  1                                                                              r                  2                                                            0                                            0                                                                                      -                                      r                    2                    *                                                                                                r                  1                  *                                                            0                                            0                                                                    0                                            0                                                              r                  3                                                                              r                  4                                                                                    0                                            0                                                              -                                      r                    4                    *                                                                                                r                  3                  *                                                              ]                                    (        6        )            
Unlike the coding matrix illustrated in Equation (4), the above coding matrix is designed to be an Alamouti STBC rather than a diagonal matrix. The use of the Alamouti STBC scheme increases the coding gain.
This Alamouti FDFR STBC, however, has the distinctive shortcoming of increased coding complexity because the transmitter needs to perform computations between all of the elements of the pre-coding matrix and an input vector, for pre-coding. For example, for four Tx antennas, since 0 is not included in the elements of the pre-coding matrix, computation must be carried out on 16 elements. Also, the receiver needs to perform ML decoding with a large volume of computation in order to decode the signal, d, transmitted by the transmitter.
To reduce such high complexity, Chan-Byoung Chae, et al. of Samsung Electronics proposed a novel STBC,
                    Θ        =                  [                                                    1                                                              α                  0                  1                                                            …                                                              α                  0                                                                                    N                        t                                            /                      2                                        -                    1                                                                              0                                            …                                            0                                                                    0                                            0                                            …                                            0                                            1                                            …                                                              α                  1                                                                                    N                        t                                            /                      2                                        -                    1                                                                                                      ⋮                                            ⋮                                            ⋰                                            …                                            …                                            ⋰                                            ⋮                                                                    1                                                              α                                                            N                      t                                        -                    2                                    1                                                            …                                                              α                                                            N                      t                                        -                    2                                                                                                      N                        t                                            /                      2                                        -                    1                                                                              0                                            …                                            0                                                                    0                                            0                                            …                                            0                                            1                                            …                                                              α                                                            N                      t                                        -                    1                                                                                                      N                        t                                            /                      2                                        -                    1                                                                                ]                                    (        7        )            where Θ is a pre-coding matrix for an arbitrary even number of Tx antennas. The subsequent operations are performed in the same manner as in Cheun's group. Yet, compared to the FDFR Alamouti STBC scheme, Chae's scheme remarkably reduces the ML decoding complexity at the receiver through a series of operations, that is, puncturing and shifting.
However, all of the approaches described above suffer from high decoding complexity relative to the Alamouti scheme that allows linear decoding of the transmitted symbols, and thus continual efforts have been made to further decrease the decoding complexity. In this context, Professor Sundar Rajan's group from India (hereinafter, referred to as Sundar Rajan group) presented an FDFR STBC that allows linear decoding.
For the Sundar Rajan group's STBC, every value ri of the coding matrix illustrated in Equation (6) is multiplied by ejθ (i.e. rotation on a complex plane), and the real and imaginary parts of the resulting new value xi+jyi are reconstructed. The coding matrix produced in this way is expressed as
                    S        =                  [                                                                                          x                    1                                    +                                      jy                    3                                                                                                                    x                    2                                    +                                      jy                    4                                                                              0                                            0                                                                                      -                                                            (                                                                        x                          2                                                +                                                  jy                          4                                                                    )                                        *                                                                                                                    (                                                                  x                        1                                            +                                              jy                        3                                                              )                                    *                                                            0                                            0                                                                    0                                            0                                                                                  x                    3                                    +                                      jy                    1                                                                                                                    x                    4                                    +                                      jy                    2                                                                                                      0                                            0                                                              -                                                            (                                                                        x                          4                                                +                                                  jy                          2                                                                    )                                        *                                                                                                                    (                                                                  x                        3                                            +                                              jy                        1                                                              )                                    *                                                              ]                                    (        8        )            
The use of Equation (8) allows for linear decoding at the receiver, thus decreasing the decoding complexity. Professor Sundar Rajan uses a fixed phase rotation angle θ. Here, θ=(1/2) a tan 2.
A mobile communication system using the Sundar Rajan group's STBC scheme adopts a transmitter having the configuration illustrated in FIG. 5. Information symbols s1, s2, s3, s4 are multiplied by exp(jθ) in a pre-coder 500 and then reconstructed in a mapper 502.
To be more specific, the mapper 502 reconstructs pre-coded symbols ci=xi+jyi to c1′=x1+jy3, c2′=x2+jy4, c3′=x3+jy1, and c4′=x4+jy2, and groups the reconstructed symbols in pairs to vectors [c2′c1′] and [c4′c3′]. The vectors [c2′c1′] and [c4′c3′] are transmitted through their corresponding Alamouti coders 506 and 508. Delay 504 is used to delay the [C4′C3′] vector.
To illustrate that the performance of the Sundar Rajan group's STBC can be further improved, a brief survey of an orthonormal space-time code and orthogonal space-time code will be given below.
To demodulate an orthonormal space-time code S proposed by Tarokh et. al., S is multiplied by its Hermitian, SH. Thus,
                              SS          H                =                  [                                                    ρ                                            0                                            0                                            0                                                                    0                                            ρ                                            0                                            0                                                                    0                                            0                                            ρ                                            0                                                                    0                                            0                                            0                                            ρ                                              ]                                    (        9        )            where ρ is a constant. If a space-time code satisfies Equation (9), it was found out that an available full rate is
                              R          max                =                              a            +            1                                2            a                                              (        10        )            
The number of Tx antennas N=2a. Therefore, for a system with four Tx antennas, a=2 and Rmax=3/4.
The Sundar Rajan group proved that its orthogonal space-time code also achieves full diversity. In this case,
                              SS          H                =                  [                                                                      ρ                  1                                                            0                                            0                                            0                                                                    0                                                              ρ                  1                                                            0                                            0                                                                    0                                            0                                                              ρ                  2                                                            0                                                                    0                                            0                                            0                                                              ρ                  2                                                              ]                                    (        11        )            where ρ1=|h1|2+|h2|2 and ρ2=|h3|2+|h4|2 (h is a channel coefficient). One thing to be noted here is that this orthogonal space-time code leads to the rate of
                              R          max                =                              2            ⁢            a                                2            a                                              (        12        )            
This equation reveals that Rmax=1 can be achieved for a system with four Tx antennas because N=2a. That is, the use of an orthogonal space-time code achieves full diversity and full rate.
Although it is theoretically impossible to design an FDFR orthogonal space-time code, it can be considered to be the upper bound of performance. This can be confirmed from the performance of a 1Rx 4Rx system. In this system, the orthogonal space-time code performs poorly, which implies that there is more room for improving the performance of the orthogonal space-time code.
To achieve full diversity and full rate in an Orthogonal Frequency Division Multiplexing (OFDM) system with three Tx antennas, the Sundar Rajan group proposed the following.
                    A        =                  [                                                                      s                  1                                                                              -                                      s                    2                    *                                                                              0                                            0                                                                                      s                  2                                                                              s                  1                  *                                                                              s                  3                                                                              -                                      s                    4                    *                                                                                                      0                                            0                                                              s                  4                                                                              s                  3                  *                                                              ]                                    (        13        )            
The above coding matrix A involves frequency and time as variables for the communication system with three Tx antennas. The rows of the coding matrix A represent the respective Tx antennas. The first two columns (si and −s*2; in the first row) are mapped to a first frequency and the last two columns (0 and 0 in the first row) to a second frequency. The former column in each of the two column pairs (s1 in the first row) is mapped to a first time interval and the latter column (−s*2; in the first row) to a second time interval. Therefore, the symbol transmitted at the second time interval at the second frequency through the second antenna is s*1 and the symbol transmitted at the first time interval at the second frequency through the third antenna is s4.